In the general context of air traffic, it is a fact that the traffic density is increasing year-on-year. At the same time, it is necessary for the environmental impact of the air traffic to be reduced. Finally, it is necessary for the accident rate to be kept at the current level, or even reduced. Respecting these principles and requirements notably requires the air traffic control organizations to exercise increasingly tight control on the flight profiles of the aircraft occupying the air space. At the same time, it is necessary for the operators of these aircraft to implement devices whose function is to satisfy the requests originating from the air traffic control organizations, while minimizing their impact, notably on the piloting procedures, the initial flight plan, and observance of the provisions in terms of aircraft operating cost.
Typically, the air traffic control organizations can impose passages at given points of the air space on the aircraft, at given times, or RTA (Requested Time of Arrival) for a scheduled time constraint or CTA (Controlled Time of Arrival) for a time constraint activated by the air traffic controller. Hereinafter, these two types of constraint will be designated RTA without distinction. To observe an RTA, the pilot of an aircraft must control the speed profile along the flight plan. To this end, there are devices known from the prior art that assist or even supplant the pilot; such devices are notably implemented in the FMSs of aircraft that are equipped therewith.
Typically, such devices determine a performance index, for example a cost index usually designated by the acronym CI, which represents the ratio between the cost in terms of flight time and the cost in terms of fuel. Other indices can be employed; these indices are determined iteratively, and define a proportionality coefficient between different speed profiles. For a given index, the proportionality coefficient is applied uniformly over the entire profile, and makes it possible to obtain, at any point of the flight plan, the speed setpoint to be applied. In a simplified manner, one process then consists in arbitrarily setting a value of the index, calculating the corresponding speed profile, and estimating the time of passage, or ETA (Estimated Time of Arrival), at the point for which the RTA is applied. The index is then corrected, and the process reiterates the calculation of the ETA according to the new speed profile resulting therefrom; this continues until the ETA is sufficiently close to the RTA according to a predetermined criterion corresponding, for example, to a desired maximum time difference. Such a method has a certain number of drawbacks:                determining the speed profile with which to observe the RTA requires a number of iterations that may be high, the number of iterations being relatively unpredictable and variable from one calculation to another;        in some cases, the convergence of the calculation of the index is difficult, because of complex behaviours of the function linking the performance index to the time of passage at the point at which the RTA is applied;        if there is a drift during a flight relative to the calculated profile, for example because of wind gusts or even unexpected aircraft performance levels, it is necessary for the calculation of the speed profile to be repeated in full. It is also necessary to ensure a relatively short periodicity in the performance of the calculation, in order to keep to precise predictions;        on approaching the point at which the RTA is applied, it becomes difficult to compensate sufficiently responsively for any drifts.        
A first method, described in the patent U.S. Pat. No. 6,507,782, allows for an adaptation of the speed profile according to a local sensitivity of the time of passage to the speed variation. However, this sensitivity is globally consolidated to compensate for the total error on the time of passage. This type of method does not call into question the principle whereby the speed profile must be determined by successive iterations, and each iteration can be likened to an open-loop calculation of the impact of the speed profile adopted on the time of passage resulting therefrom. Furthermore, drifts exhibited during the flight are compensated according to the same method, by iterations over the entire speed profile ahead of the aeroplane.
A second method, described in the patent U.S. Pat. No. 5,121,325, consists in varying the precision margins on the observance of the time of passage, as a function of time, so as not to unnecessarily constrain the speed profile when the aircraft is far from the constraint associated with the RTA, and on the other hand to increase the precision on approaching this point. This method makes it possible to optimize the profile, and improve confidence in the observance of the time constraint imposed by an RTA. On the other hand, this method also relies on an open-loop speed prediction, the slaving to the time of passage being based only on a calculation of predictions relating to the flight plan as a whole.